Spectral Distortion in Lattice Filters (#ARIJIT BISWAS# )

Subject: Spectral Distortion in Lattice Filters From: #ARIJIT BISWAS# <arijit17(at)PMAIL.NTU.EDU.SG> Date: Tue, 22 Nov 2005 17:02:00 +0800 This is a multi-part message in MIME format. ------_=_NextPart_001_01C5EF43.EA4419C3 Content-Type: text/plain; charset="iso-8859-1" Content-Transfer-Encoding: quoted-printable Dear Members of the list: =20 My question is related to quantization of Linear Prediction (LP) = Parameters. =20 I know very well that LP parameters are mapped onto Reflection = Coefficients and we get a lattice filter. =20 Now, lets say I have an order K Lattice filter: implying that I've a = concatenation of first-order lattice filters. =20 If we quantize the parameters (i.e. the reflection coefficients) of each = these first-order sections we get a Spectral Distortion associated with = it, say D_k (k =3D 1,2,....,K). I would like to know if there is any = straightforward relationship between these first-order Spectral = Distortions to the overall Spectral Distortion in an order-K system.=20 For example, lets say, D_total =3D D_1 + D_2 +...... + D_K. =20 Is there any work done on this field? Is it possible to predict the = overall distortion just from the knowledge of the distortion in the = first-order section?=20 =20 I'll be extremely grateful if someone can cite some references or maybe = some indication on the overall distortion.=20 =20 Best Regards, ~Arijit ------_=_NextPart_001_01C5EF43.EA4419C3 Content-Type: text/html; charset="iso-8859-1" Content-Transfer-Encoding: quoted-printable <META HTTP-EQUIV=3D"Content-Type" CONTENT=3D"text/html; = charset=3Diso-8859-1">=0A= <!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 3.2//EN">=0A= <HTML>=0A= <HEAD>=0A= =0A= <META NAME=3D"Generator" CONTENT=3D"MS Exchange Server version = 6.5.7638.1">=0A= <TITLE>Re: head directivity data & phoneme spectral statistic</TITLE>=0A= </HEAD>=0A= <BODY>=0A= <DIV id=3DidOWAReplyText76800 dir=3Dltr>=0A= <DIV dir=3Dltr><SPAN lang=3DEN-US =0A= style=3D"FONT-SIZE: 10pt; FONT-FAMILY: Verdana; mso-ansi-language: = EN-US; mso-fareast-font-family: 'Times New Roman'; mso-fareast-language: = EN-US; mso-bidi-language: AR-SA; mso-bidi-font-size: 12.0pt; = mso-bidi-font-family: 'Times New Roman'">=0A= Dear =0A= Members of the list:<?xml:namespace =0A= prefix =3D o ns =3D "urn:schemas-microsoft-com:office:office" =0A= /><o:p></o:p>=0A=  <o:p></o:p>=0A= My =0A= question is related to quantization of Linear Prediction (LP) =0A= Parameters.<o:p></o:p>=0A=  <o:p></o:p>=0A= I know =0A= very well that LP parameters are mapped onto Reflection Coefficients and = we get =0A= a lattice filter.<o:p></o:p>=0A=  <o:p></o:p>=0A= Now, =0A= lets say I have an order K Lattice filter: implying that I’ve a = concatenation of =0A= first-order lattice filters.<o:p></o:p>=0A=  <o:p></o:p>=0A= If we =0A= quantize the parameters (i.e. the reflection coefficients) of each these =0A= first-order sections we get a Spectral Distortion associated with it, = say D_k (k =0A= =3D 1,2,….,K). I would like to know if there is any = straightforward relationship =0A= between these first-order Spectral Distortions to the overall Spectral =0A= Distortion in an order-K system. <o:p></o:p>=0A= For =0A= example, lets say, D_total =3D D_1 + D_2 +…… + = D_K.<o:p></o:p>=0A=  <o:p></o:p>=0A= Is =0A= there any work done on this field? Is it possible to predict the overall =0A= distortion just from the knowledge of the distortion in the first-order = section? =0A= <o:p></o:p>=0A=  <o:p></o:p>=0A= I’ll =0A= be extremely grateful if someone can cite some references or maybe some =0A= indication on the overall distortion. <o:p></o:p>=0A=  <o:p></o:p>=0A= Best =0A= Regards,<o:p></o:p><SPAN lang=3DEN-US =0A= style=3D"FONT-SIZE: 10pt; FONT-FAMILY: Verdana; mso-ansi-language: = EN-US; mso-fareast-font-family: 'Times New Roman'; mso-fareast-language: = EN-US; mso-bidi-language: AR-SA; mso-bidi-font-size: 12.0pt; = mso-bidi-font-family: 'Times New = Roman'">~Arijit</DIV></DIV>=0A= =0A= </BODY>=0A= </HTML> ------_=_NextPart_001_01C5EF43.EA4419C3--

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DAn Ellis <dpwe@ee.columbia.edu>
Electrical Engineering Dept., Columbia University